Answer
$\displaystyle 2x+h$
Work Step by Step
We are given:
$f(x)=x^{2}-4$
We find the difference quotient:
$\frac{f(x+h)-f(x)}{h}$
$\displaystyle =\frac{(x+h)^{2}-4-(x^{2}-4)}{h}$
$\displaystyle =\frac{x^{2}+2xh+h^{2}-4-x^{2}+4}{h}$
$\displaystyle =\frac{2xh+h^{2}}{h}$
$\displaystyle =\frac{h(2x+h)}{h}$
$\displaystyle =2x+h$